The present invention relates to a system for converting a digital audio data recorded at a sampling frequency to a digital data to be sampled at another sampling frequency, and a method thereof.
There are provided various types of digital audio systems, for example, compact discs (CDs) and digital-audio tape (DAT). Each system uses different sampling frequency (sampling rate) such as 96 kHz, 88.2 kHz, 48 kHz, 44.1 kHz, and 32 kHz. In order to record the digital data originally recorded on a digital audio system on another system, the original data must be converted into data at another frequency.
The most simple method for converting the digital data is to convert the digital data signal into an analog data signal. The analog data signal is further converted into a digital data signal at a desired sampling frequency which is different from the original sampling frequency. However, in the course of the conversion, noises and jitters are generated, thereby inevitably deteriorating and changing the sound quality.
There has been a demand for a method where the digital data is digitally processed to obtain another digital data.
The principle of one of the conventional method for converting the digital data having a sampling frequency fa Hz into a digital data having a sampling frequency fb Hz is described. First of all, the number of the sampling points is increased to the value of the least common multiple between the sampling frequencies fa and fb Hz. The number of the sampling points is decreased so that the number correspond to the sampling frequency fb Hz.
However, when these processes are carried out, noise due to an aliasing error is generated. In order to restrain the noise, the sampling is performed in accordance with the sampling theorem, or performed so that the noise is canceled. Moreover, an extremely large amount of calculation is necessary to precisely execute the process. Ingenious steps to decrease the calculation must be taken to put the method into actual use in hardware.
One of the conventional converting method is called a synchronous direct conversion method. For example, the method for converting the sampling frequency at a rate of 3/2 is described hereinafter with reference to FIGS. 31a to 31e, showing the changes in the spectrum of the data when the sampling frequency is converted.
First of all, two zero data are inserted in the two sampling point (sampled digital data) of the original digital data signal shown in FIG. 31a. Thereafter, the sampling frequency is expanded triple, namely, triple over-sampling is performed. FIG. 31b shows the spectrum after the insertion in accordance with the z transform and Fourier transformation.
Thereafter, an image component, which is generated upon the triple over-sampling, is removed by a low-pass filter (LPF) having a one-third band width as shown in FIG. 31d. Since the level of the direct current is reduced to one-third of the original level when the zero data are inserted, the triple DC gain of the LPF is imparted at the present step as shown in FIG. 31c.
At the next step, the number of sampling is reduced to one half, that is, one-half down-sampling is performed, by taking one data out of two. Thus as shown in FIG. 31e, the conversion of the sampling frequency is completed.
In another example, the sampling frequency is converted at the rate of 2/3 as shown in FIGS. 32a to 32e.
One zero data is inserted in the sampling point so that the sampling frequency is doubled. Namely, double over-sampling is performed. Thus the original spectrum shown in FIG. 32a is converted into the spectrum shown in FIG. 32b in accordance with the z transform and the Fourier formation.
Thereafter, an image component, which is generated upon the double over-sampling, is removed by the LPF having a one-third band width as shown in FIG. 32d. Since the level of direct current is reduced by one-half when the zero data are inserted, the double DC gain of the LPF is imparted at the present step as shown in FIG. 32c.
At the next step, the number of sampling is reduced to one-third, that is, one-third down-sampling is performed, by taking one data out of three. Thus as shown in FIG. 32e, the conversion of the sampling frequency is completed.
As described above the method of converting the sampling frequency at a rate of L/M where L and M are natural numbers, can be generalized as follows.
(1) (L-1) number of zero data are inserted in adjacent sampling point so that the sampling frequency is increased L times. PA1 (2) An LPF having either a 1/L band width or a 1/M band width whichever is narrower, is used to remove an image component generated during the over-sampling. Since the DC level is reduced to 1/L when the zero data are inserted, the DC gain of the LPF is L times. PA1 (3) One data out of M sampling data is taken, thereby decreasing the number of sampling to 1/M.
Although the LPF used in the case of converting at the rate L/M and the LPF used in the case of converting at the rate M/L differ in DC gains, they have the same cutoff frequency.
FIG. 33a shows a block diagram of a sampling frequency converting system for converting the sampling frequency in accordance with the synchronous direct conversion method. The system comprises a fixed sampling frequency changing rate converter 31 and phase-locked loop (PLL) circuit 32 to which is connected an oscillator 33, the oscillating frequency of which is variable. The input signal is applied both to the converter 31 and the PLL circuit 32 so that the timings of the input signal and the output signal are synchronized.
As shown in a graph (i) in FIG. 33b, the data of the input signal are sampled at the sampling points indicated by white dots. When converting the sampling frequency at the rate of 3/2, the sampling points are increased three times as shown by xs in a graph (ii). Every other point is selected as shown in black dots in a graph (iii) to obtain digital data wherein the sampling frequency is converted.
Since the conversion rate is fixed, the accuracy of the synchronous direct converting method depends on the precision of the LPF as the conversion filter. Moreover, in order to synchronize the input and output signals of the fixed sampling frequency changing rate converter 31, it is necessary to provide the PLL circuit 32. Hence the conversion accuracy is not affected by a time jitter of the input signal. Namely, the same process as that executed in a computer is carried out.
In the above described synchronous direct conversion method, a large amount of calculation is required although the conversion is carried out at a single fixed rate. In order to render it possible to convert the sampling frequency at various rates, the amount of calculation must be further increased. Hence it is difficult to provide hardware capable of performing such a conversion.
Moreover, there are cases where it is necessary that the input and output signals of the converter are asynchronous with each other, such as when converting video signals.
On account of these problems, most of the sampling frequency conversion systems which are currently on the market use asynchronous indirect conversion method.
In the asynchronous indirect conversion method, the sampling frequency of the output signal is a fixed desired frequency. When input signals having various sampling frequencies are applied to the conversion system, the sampling frequency thereof detected by some means or other and the conversion rate is adaptively changed as necessary. Since the conversion rate is variable, it is impossible to provide the system with conversion filters for every possible situation.
Referring to FIG. 35a, an asynchronous indirect conversion system comprises a variable sampling frequency changing rate converter 34, and a counter 35 to which is connected an oscillator 36 generating a signal at a fixed frequency. The counter 35 counts a sampling frequency of the input signal by a sampling frequency of the output signal.
As shown in a graph (i) of FIG. 35b, the input signal, the sampling points of which are shown by the white dots, is over-sampled by a power of 2, for example, amounting to several hundreds, for the ease of the processing.
The input frequency is converted using the output frequency as shown in the graph (ii). The signal undergoes such process as averaging so that the conversion rate is determined. As shown in the graph (iii), the data at the sampling points indicated by triangles is determined in accordance with the adjacent sampling points indicated by the black dots by a simple process such as linear interpolation.
More specifically, in order to convert the sampling frequency at the rate of 3/2 times, the input signal is double over-sampled and the data at the desired sampling points are calculated by linear interpolation.
In the asynchronous in direct conversion method, the PLL circuit is not necessary, and a conventional over-sampling IC can be used for over-sampling. Hence the method can be easily applied to hardware and ICs. In addition, input signals with jitters are processed by changing th e conversion rate, the clocking precision is increased. Hence the converter also serves as a jitter reducer.
FIG. 34 shows a table showing the conversion rates in principle between the input sampling frequencies and output sampling frequencies. As seen from the table, if the asynchronous indirect conversion is to be carried out to the principle, over-sampling with a conversion filter as much as 320 times at maximum becomes necessary. This requires the conversion filter to be provided with more than 30,000 taps if the precision of 24 bits is to be realized.
FIG. 36 shows a spectrum of an audio signal of 10.007 kHz in the form of a sine wave reproduced from a CD, the sampling frequency of which 44.1 kHz, and converted into an audio signal having a sampling frequency of 48 kHz. As shown in the graph, the spectrum after the conversion changes with time so that the main lobe is expanded. Hence the desired precision is not obtained.
In the synchronous direct conversion method, the spectrum of the signal changes after the conversion so that it is impossible to achieve a desired precision in principle. In addition, the synchronous direct conversion is effective in the cases where digital data are converted into analog data, and vice versa. In the case of digital to digital conversion, the conversion rate is changed to absorb the jitters and the absolute differences. Therefore, the frequency components of the resultant signal differs from those of the original signal. The sound quality is inevitably deteriorated.
Another problem inherent in the conventional conversion system is that, in order to improve the accuracy of the conversion, the over-sampling must be performed before the conversion at a large number. Namely, for the purpose of obtaining a precision of about 20 bits, the over-sampling must be performed at several hundred times at the least. If more precise conversion is required, the scale of the hardware must be increased. Moreover, since the conversion rate is calculated in accordance with the input and output clock, the source having jitters cannot be accurately converted.
In order to solve these problems, it is conceivable to use a synchronous indirect conversion method. However, the over-sampling must still be performed at a large number to increase the accuracy, thereby increasing the scale of the hardware.